Question 194
Denote by $m_a$, $m_b$, $m_c$, respectively, the lengths of the medians from the vertices $A$, $B$, $C$ of a triangle $ABC$ to the opposite sides, respectively. Prove that
$$
m_a + m_b + m_c \geq a \sin A + b \sin B + c \sin C
$$
with equality iff the triangle is equilateral.
$$
m_a + m_b + m_c \geq a \sin A + b \sin B + c \sin C
$$
with equality iff the triangle is equilateral.